The point made by Brillouin in his book and by other famous names in the 50's was precisely to restrict the concept of information to a scientific concept. Therefore it is all about measurable things, not about the content and its subjective meaning. Brillouin, in his introduction, precisely points out that an amount of information can have a high meaning for some people and no meaning at all for others.
However, I thing this is merely a practical limitation of physics. Human aspects are often too complex. It is clear that an information can also have a huge effect on a certain computer and no effect at all on another one, because of the configuration. In a sense this is computer-subjectivity. And on this computer toy-model, it is clear that the 'importance' of an information can also be quantified, just by the same tools as those devised in the 50's before computers where available everywhere.